## 22681Re: [PrimeNumbers] Products of k distinct primes that are concatenations of first k: Coincidence

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• Apr 4, 2011
Sorry if I was a bit unclear.  The title was supposed to indicate what the meaning of the post was.  The ten numbers are concatenations of the first ten primes that are also products of ten distinct primes.  I have run the more efficient version on the case k=11, so that's done.  For k=2 through 11, the only examples are the ones given.  I've also now determined that the way I have programmed this so far is backwards, and that k=16 as a limit is probably very pessimistic.  The initial program used 'if(isquarefree(n),if(numdiv(n)==2^k..', and my more efficient one basically factors up until a concatenation is no longer a plausible solution; but, of course, it would be a lot more sensible--and more difficult to optimize--to look for matches of products with possible initial and/or terminal digit strings.  I would now guess that the problem can be fully worked out perhaps as far as k=25 (optimally programmed using massive currently available
resources).
JGM

--- On Mon, 4/4/11, James Merickel <merk7777777@...> wrote:

From: James Merickel <merk7777777@...>
Subject: [PrimeNumbers] Products of k distinct primes that are concatenations of first k: Coincidence
Date: Monday, April 4, 2011, 3:05 AM

1319732172923115
1713323729219115
2191317297323115
2291117192373135
2291772319133115
2322931117719135
2329131171719235
7112917313223195
7191317229231135
7191331129217235

These are the only values through k=10 (k>1).  I have a very inefficient program and a much better one for k=11 and 12, respectively, running.  I expect a null result, but will report if something comes out (couple of days).  I think the problem is tractable with maximal resources and ideal programming through about k=16.  Looking for either a further example or a heuristic proof one likely doesn't exist.

JGM

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